As a block of this kind, a block (1) is disclosed in WO00/43606. In this case, the block is formed with engaging parts (2, 2), a fitting protrusion (3), a fitting groove (4), and an insertion hole (5), and a plurality of blocks (1) can be stacked one upon another to thereby assemble a wall (structure) of a house or the like. To assemble these blocks (1) into a structure, while connecting laterally adjacent blocks (1) by fitting the engaging parts thereof to each other, each of the blocks (1) is stacked on another block positioned immediately below by fitting the fitting groove thereof on the fitting protrusion of the block positioned immediately below. This method makes it possible to assemble a highly airtight structure which is capable of preventing infiltration of rain water.